It's an interesting study. 1.1 million adults with Covid-19. 1 in 16 had Long Covid - 6.2%. That sounds reasonable, not the ridiculous percentages (e.g. 50%) that we have seen reported from some studies. I don't know how they defined Long Covid.
However some of those risk factors (i.e. of: female, older, higher BMI, more deprived, severe Covid-19, worse health (co-morbidities, prescriptions) suggest that "Long Covid" is including a lot of people with post-covid symptoms that are probably related to non-ME/CFS causes e.g. lung damage.
That finding of parenteral anticoagulants helping is intriguing. Is there anything about people taking parenteral anticoagulants that could confound the theory that the drug is protective against Long Covid once a person has contracted Covid-19? For example, perhaps they were resting at the time of the Covid-19, rather than trying to push through the illness?
It's interesting to look at the drugs that were associated with increased risk too. A number of them look to be related to allergies.